An airplane is heading north at an airspeed of 700 km/hr, but there is a wind blowing from the northeast at 40 km/hr.
The plane will end up flying ______ degrees off course.
The plane's speed relative to the ground will be _____ km/hr.
Break the two speeds into their x and y components...then add them together
Airplane ax=0 ay=700
Wind wx= -40 cos45 wy= -40sin45 (see diagram)
= -28.28 = -28.28
Add together for the RESULTANT
x=-28.28 y = 700-28.28= 671.71
Degrees off course will be arctan (-28.28/671.71) = 2.41 degrees off course to the west
Speed will be sqrt ( x^2 + y^2) = 672.3 km/hr